Poma, Flavia2012-10-222012-10-222012-10-08https://openscience.sissa.it/handle/1963/627942 pages, 6 sections, 2 appendices. Preliminary version, comments welcome. arXiv admin note: substantial text overlap with arXiv:1110.6395We define Gromov-Witten classes and invariants of smooth proper tame Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth proper tame Deligne-Mumford stack over a Dedekind domain, we prove that the invariants of fibers in different characteristics are the same. We show that genus zero Gromov-Witten invariants define a potential which satisfies the WDVV equation and we deduce from this a reconstruction theorem for genus zero Gromov-Witten invariants in arbitrary characteristic.enPreprintGromov-Witten invariantsvirtual classintersection theoryalgebraic stackquantum productMAT/03 GEOMETRIA